Zsolt Szűcs Department of Applied Analysis, Eötvös L. University, Pázmány Péter sétány 1/C, 1117 Budapest, Hungary

Search for other papers by Zsolt Szűcs in
Current site
Google Scholar
Restricted access


Our purpose is to show that the various concepts of singularity of representable positive functionals on -algebras coincide, moreover to present a new characterization of singularity by means of Choquet theory of the state space. In the context of singularity, the paper includes an equivalent condition for a representable positive functional to be pure.

  • [1] Bratelli, O. Robinson, D. W. 2002 Operator Algebras and Quantum Statistical Mechanics, Vol I. C- and W-Algebras, Symmetry Groups, Decomposition of States 2 Texts and Monographs in Physics Springer-Verlag New York–Heidelberg.

    • Search Google Scholar
    • Export Citation
  • [2] Dixmier, J. 1977 C -algebras North-Holland Mathematical Library 15 North-Holland publishing Co. Amsterdam–New York–Oxford Translated from the French by F. Jellett.

    • Search Google Scholar
    • Export Citation
  • [3] Gudder, S. P. 1979 A Radon–Nikodym theorem for -algebras Pacific J. Math. 80 141149.

  • [4] Handel van, R. 2009 The stability of quantum Markov filters Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12 153172 .

  • [5] Hassi, S. Sebestyén, Z. Snoo de, H. 2009 Lebesgue type decompositions for nonnegative forms J. Functional Analysis 257 38583894 .

  • [6] Henle, M. 1972 A Lebesgue decomposition theorem for C-algebras Canad. Math. Bull. 15 8791 .

  • [7] Hewitt, E. Ross, K. A. 1970 Abstract Harmonic Analysis. Vol. II.: Structure and Analysis for Compact Groups. Analysis on Locally Abelian Compact Groups Die Grundlehren de Mathematischen Wissenschaften 152 Springer-Verlag New York–Berlin.

    • Search Google Scholar
    • Export Citation
  • [8] Kosaki, H. 1985 Lebesgue decomposition of states on a von Neumann algebra American J. Math. 107 697735 .

  • [9] Palmer, T. W. 2001 Banach Algebras and the General Theory of -Algebras II Cambridge University Press.

  • [10] Pedersen, G. K. 1979 C -Algebras and their Automorhpism Groups London Mathematical Society Monographs 14 Academic Press, Inc. London–New York Hartcourt Brace Jovanovich, Publishers.

    • Search Google Scholar
    • Export Citation
  • [11] Sebestyén, Z. 1984 On representability of linear functionals on -algebras Period. Math. Hungar. 15 233239 .

  • [12] Szűcs, Zs., On the Lebesgue decomposition of positive linear functionals, Proc. Amer. Math. Soc., to appear.

  • [13] Szűcs, Zs., The Lebesgue decomposition of representable forms over algebras, J. Operator Theory, to appear.

  • [14] Takesaki, M. 2002 Theory of Operator Algebras I Encyclopaedia of Mathematical Sciences 124 Springer-Verlag Berlin.

  • Collapse
  • Expand

To see the editorial board, please visit the website of Springer Nature.

Manuscript Submission: HERE

For subscription options, please visit the website of Springer Nature.

Acta Mathematica Hungarica
Language English
Size B5
Year of
per Year
per Year
Founder Magyar Tudományos Akadémia  
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Dec 2023 11 1 0
Jan 2024 19 1 0
Feb 2024 21 1 0
Mar 2024 6 0 0
Apr 2024 7 0 0
May 2024 72 0 0
Jun 2024 0 0 0